Theresa May will be accompanied by Boris Johnson (left) in Florence.
Photograph: Lucas Jackson/Reuters

Theresa May will call on EU leaders to be more “imaginative and creative” about Brexit in her long-awaited speech in Florence, after Michel Barnier, the EU’s chief negotiator, warned that a substantive offer to settle the UK’s bills was needed to break the deadlock in talks.

The prime minister will urge her European counterparts to share her vision for building a successful new relationship between the UK and EU after Brexit, despite talks with the European commission negotiators having reached a stalemate after three rounds.

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Addressing her remarks to other EU leaders, rather than the commission, May will tell them they all have a “profound sense of responsibility to make this change work smoothly and sensibly” by reaching a deal.

“If we can do that, then when this chapter of our European history is written, it will be remembered not for the differences we faced, but for the vision we showed; not for the challenges we endured but for the creativity we used to overcome them; not for a relationship that ended but a new partnership that began,” she will say.

“The eyes of the world are on us but if we can be imaginative and creative about the way we establish this new relationship, I believe we can be optimistic about the future we can build for the United Kingdom and for the European Union.”

May is not likely to bow to all the demands of her foreign secretary, whose friends said this week that he could resign if she set out proposals to stay too close to the single market in a relationship with the EU akin to Switzerland’s.

However, she will rule out using any existing template for the relationship and pledge to pursue a bespoke deal.

She is also likely to make an offer to ensure no country has to pay more into the budget until 2020 as a result of Brexit, without committing to permanent payments to the EU. Her proposal would involve the UK continuing to pay into the EU during its transitional period after leaving the bloc in March 2019 at a cost of around €20bn (£17.5bn).

The payments during the transition period would be conditional on continued access to the single market and a customs union arrangement which did not stop the UK beginning to negotiate its own trade deals.

She is likely to say that Britain wants a transitional period, possibly lasting two years, to smooth the path of leaving the EU for businesses.

May is also expected to offer greater protections for EU citizens living in the UK by ensuring their rights are enshrined in the Brexit treaty, enforced by UK courts.

However, Barnier issued a fresh warning on Thursday that May’s offer to the rest of Europe must be detailed and substantial enough for talks to progress once they restart on Monday.

Warning that the UK had just one year left to make a deal, he said: “The question facing us over the coming months is serious, but simple: will the United Kingdom leave in an orderly fashion with an agreement, or not?

“From our side, I repeat once again that an agreement is the best outcome. It is in our common interest. But if we want a deal, time is of the essence.”

He said the three key issues that still had to be resolved before talks could move on to trade were the financial settlement, the rights of EU citizens and the Irish border.

“We are a few days away from the fourth round of negotiations,” Barnier said.

“I am asking myself questions. I’m wondering why – beyond the progress we’ve made on certain points – there is still today major uncertainty on each of the key issues of the first phase.

“To make progress, we are waiting for clear commitments from the UK on these precise issues. We will listen attentively and constructively to Theresa May’s important speech tomorrow in Florence.”

Barnier warned that May would have to make a substantive offer on citizens’ rights and the financial settlement to break the deadlock, as well as repeating the view that the UK would have to accept EU rules during any transitional period.

Sources who have seen May’s speech told the Guardian that the prime minister would give an update on policy but there were worries that its significance had been overhyped and there was a last-minute attempt under way to make its tone more visionary.

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Another Conservative politician said the signs from Downing Street were that the speech would be a “damp squib” because there had been too many compromises to appease the warring factions in cabinet.

May will be accompanied in Florence by Johnson, as well as Philip Hammond, the chancellor, and David Davis, the Brexit secretary, in an unusual show of public unity, but securing cross-cabinet approval has been difficult.

The prime minister reached an agreement on the contents of her speech in a two-and-a-half-hour cabinet meeting in Downing Street on Thursday, after a week of tensions with Johnson and other former leave campaigners over the direction of Brexit.

Johnson and Hammond left the meeting together in what appeared to be a coordinated show of togetherness, despite representing the two opposing cabinet factions. Johnson rejects the idea of retaining regulatory equivalence to the EU in the long term and has cited Canada as a possible model for the UK’s relationship with the EU in future. He is also unhappy with the idea of permanent payments to the EU budget.

On the other side, Hammond and a number of other ministers want to prioritise remaining as close to the single market as possible and in a customs union, a model that would be closer to Switzerland’s relationship with the EU.

However, the senior cabinet minister David Gauke insisted after the meeting that the cabinet was united on the plan. “The PM has the backing of us all,” he said.

Although May claims to have united the cabinet, some backbench Tory Eurosceptics will not be happy with the idea of any more payments to the EU after the point of departure.

Peter Bone, a Brexit supporter, told Sky: “Any divorce bill would be too much for me ... If you ask my constituents, in Wellingborough we want an urgent care centre. We’ve been campaigning for years, and it’s a few million pounds. And we are told there is not enough money for that.

“If we’re then told we’re giving £20bn to subsidise Romania and Poland, I think my constituents, and I think constituents around the country, would be furious about that.”